How to parent one vertex group to a specific bone in Blender 2.8
In my opinion you’re not working with the good method, if you were you would not ask some of these questions, but to answer:

I don't think there's any way to see what is the bone affecting a group of randomly selected vertices, because for example a group of vertices may be affected by several bones and each will have a different influence, so I it may be technically possible to display them but it won’t help a lot.

That said, you can see what bones affect one particular vertex, and how much they affect if, if you select the vertex and open the N panel > Item tab > Vertex Weights.



It's a bit tedious though and I don't think that's what you want.

The easiest way to know how bones affect vertices: Select your armature, switch to Pose mode, then shift select your object, switch it to Weight Paint mode, then select a bone and visually see its influence on the mesh. Also in that same mode, if you select a vertex group in the Vertex Groups list, you’ll see what part of the object it enlights. But you may miss some small influences because at a low value the weight won’t be visually noticeable.



But as I say I’m not sure you use the good logic to rig.

When you parent your object to your armature With Automatic Weight, the vertex groups will be automatically created with the name of the bones that control them.

Once done you can check the bones influences, and you can correct it, either in Weight Paint mode, or giving more or less weight to some vertices with the Assign or Remove button on the bottom of the Vertex Groups list. Or even use the N panel if you like this mode, but again, a bit tedious.



You can always create an additional bone. Give it the name you want. If you want some vertices to be affected by this bone, select them, create a new vertex group with the name of the bone, and click Assign. As the mesh is parent With Automatic Weight this vertex group will automatically be controlled by the bone that has the same name. And again you can play with the weight value to increase or decrease the influence.

You can also create a vertex group and create its bone afterwards, as long as it has the same name as the vertex group, it will control it.